Weird. I can only think of a few minor points where they overlap.
Even the most powerful high-end pulp heroes are peanuts compared to your bog-standard superhero. The most powerful pulp heroes are at best absurdly low-powered street-level superheroes. And that's basically the only place they overlap.
If you only look at low-powered street-level superheroes, you can kind of squint and see pulp heroes. But then you place that character in their proper setting, and all bets are off. Pulp heroes a la The Shadow, Doc Savage, The Spider, Secret Agent X, etc are quite limited in their setting when compared to superheroes. Typically you have mostly real-world 1930s-1950s settings with the occasional fantastical location on the planet in the pulps whereas in superhero stories you have alien planets, time travel, alternate dimensions, alternate realities, etc. Anything goes.
As for the villains, in the pulps you'll very occasionally have a genius-level villain with some kind of laughably basic super-science device threatening some convoluted plan to take over a piece of the planet or the whole shebang. The villains are mostly normal people with guns, a few racist stereotypes, and the occasional robot. It's rare to have a villain that's powered. In superhero stories? Wow. All bets are off. Aliens, mecha, kaiju, super-powered villains, sentient planets, demons, proper wizards as opposed to fancy stage magicians, undead, etc. Again, anything goes.
Then there's the morality. In the pulps, the heroes have zero qualms about straight up killing the bad guys or putting them into situations where their evil choices result in their deaths. Like rigging a gun to explode if fired then leaving it for the villain to find. Then there's Doc Savage's infamous Crime College and giving criminals lobotomies so they reform. Pulp heroes would be, at best, anti-heroes in a superhero world. And, of course, most of your classic superheroes are all about the high-minded morality and codes against killing, etc.
Looking at Batman, the poster boy for confusing the two, is a great place to start. He's a direct rip-off of the Shadow with some minor changes. The creators of Batman admitted this decades ago (
link 1,
link 2). In the more low-key stories Bats is challenged by mundane serial killers who occasionally wear funny pajamas but in the more absurd stories he's outwitting literal gods...and he has workable contingency plans to take out every super-powered person he's aware of. The former are closer to pulp hero stories, but Bats exists in an obviously superhero setting and his abilities are far beyond anything a pulp hero could manage.
Then there's all the differences the medium makes. Generally speaking, short prose novels vs 22-page comic books.
So what makes them distinct? Literally everything about both genres except the fact that the main character is exceptional in some way.
Not to put too fine a point on it, it's like looking at military sci-fi and space opera and saying they're the same because they both have spaceships. They're not at all the same despite having a select few elements in common.
Exactly. There's also a difference between superhero fiction and action-adventure. Just because the action-adventure hero can survive absurd events doesn't make them a superhero. Again, it's reductive. There's so much more to genre than what few traits the main characters share.